Oscillatory bubbles induced by geometrical constraint

Microscale process engineering requires precise control of bubbles and droplets. We investigate geometry-induced control and find that a centered constriction in the cross section of rectangular tubes can lead to new families of steadily propagating bubbles, which localize in the least-constricted regions of the cross section. Tuning the constriction geometry can cause a switchlike transition from centered to localized bubbles at a critical value of the flow rate: a mechanism for flow-rate-driven bubble control [1]. Striking and robust periodic oscillations develop on the advancing air-fluid interface that can dramatically reduce the volume of fluid extracted. The dynamics of the oscillations are consistent with their arising from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution.\\[4pt] [1] A. de L\'{o}zar, A. Heap, F. Box, A.L. Hazel \& A. Juel {\em Partially-occluded tubes can force switch-like transitions in the behavior of propagating bubbles}, Phys.\ Fluids. {\bf 21}, 101702; doi: 10.1063/1.3247879, 2009.